Educational Codeforces Round 32 |
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Finished |

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bitmasks

constructive algorithms

data structures

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G. Xor-MST

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given a complete undirected graph with *n* vertices. A number *a*_{i} is assigned to each vertex, and the weight of an edge between vertices *i* and *j* is equal to *a*_{i} *xor* *a*_{j}.

Calculate the weight of the minimum spanning tree in this graph.

Input

The first line contains *n* (1 ≤ *n* ≤ 200000) — the number of vertices in the graph.

The second line contains *n* integers *a*_{1}, *a*_{2}, ..., *a*_{n} (0 ≤ *a*_{i} < 2^{30}) — the numbers assigned to the vertices.

Output

Print one number — the weight of the minimum spanning tree in the graph.

Examples

Input

5

1 2 3 4 5

Output

8

Input

4

1 2 3 4

Output

8

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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